Y=-x(2x-5)

Solution for Y=-x(2x-5) equation:

=-Y(2Y-5)

We move all terms to the left:

-(-Y(2Y-5))=0


We calculate terms in parentheses: -(-Y(2Y-5)), so:

-Y(2Y-5)

We multiply parentheses

-2Y^2+5Y

Back to the equation:

-(-2Y^2+5Y)


We get rid of parentheses

2Y^2-5Y=0

a = 2; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·2·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*2}=\frac{0}{4}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*2}=\frac{10}{4}
=2+1/2
$